As they seek to prove big crimes, prosecutors must present large amounts of evidence, some of it complex. But persuading juries also requires a simple theory of the case that shows how the evidence fits together, and the best way to do that is it give jurors catchy details to help them understand the narrative — and find the defendants guilty.

By that standard, prosecutors are hitting the motherlode in the ballooning New York corruption scandal. Among the seal-the-deal details are elves and hookers, garbage bags and fancy Italian bags, a private jet and a private lane in the Lincoln Tunnel.

And if Mayor Bill de Blasio is next in the dock, expect the charges to include references to a different kind of bag — rodent-resistant garbage bags, among other unappealing examples.

The details and the scope of the cases are making this one of the most remarkable municipal scandals ever. The $20 million involved in the arrest of the former head of the corrections union, and the shocking favoritism and bribes alleged at the top ranks of the NYPD, would each constitute a milestone on their own.

But because they are linked, and because one of the players in both cases was a major donor to the mayor and is singing to prosecutors, Gotham could be making history of the worst kind.

The arrests show state and federal prosecutors moving up the food chain, from little fish to bigger fish. That has to be scaring the bejesus out of the biggest fish.

For one thing, the prosecutors are playing hardball. They’re not trying to scare anybody straight; they’re leading with handcuffs.

For another, they’ve uncovered an astonishing array of alleged criminal behavior. Norman Seabook, the former union boss, was charged with demanding kickbacks for investing $20 million of pension money, and prosecutors said $60,000 was delivered in the Ferragamo bag.

The man who says he was the bag man, businessman Jona Rechnitz, pleaded guilty to conspiracy and is cooperating — and the feds say they found the Ferragamo bag in Seabrook’s house. If the case goes to trial, Rechnitz’s testimony and the actual bag would be powerful evidence for any jury.

Similarly, with the cops, the bribery would be easy for a jury to understand, according to the charges. Two businessmen gave them wads of cash, a private jet trip to the Super Bowl (hooker included), expensive jewelry, home repairs, sports tickets.

For their $100,000 in “gifts,” the businessmen got “a private police force for themselves and their friends,” said US Attorney Preet Bharara. The “cops on call” even shut down a lane of the Lincoln Tunnel and escorted a friend of the businessmen into the city, he charged.

All those things are easily documented, and with wiretapped conversations included, a jury likely would lean toward prosecutors. Who can forget elf hats and hookers? And what juror wouldn’t find something wrong with a cop getting a private jet ride and giving a rich businessman his own traffic lane?

The mayor hasn’t been charged, but as one lawyer said to me yesterday, “he has to feel the noose tightening.” While Rechnitz was a big donor to the mayor, it’s not clear what, if anything, he got in return.

However, other big donors got clear favors, and with many millions raised from people with matters before City Hall, prosecutors have tons of potential evidence. They’re gathering documents through subpoenas and interviewing individual donors.

As with Seabrook and the cops, the test will be whether prosecutors can show that de Blasio engaged in a quid pro quo with donors. It also could be a crime if the donors believed they had to give to the mayor simply to be treated fairly.

Among the catchy details, some donors gave hundreds of thousands of dollars while having business before the city that was worth millions. That would get a jury’s attention.

Then there’s the trash bags. Owner Joseph Dussich couldn’t get the time of day from City Hall until he contributed $100,000 to de Blasio’s slush fund, then got a meeting with the mayor and two contracts.

The bags might come in handy, and not just to a jury. They could be used to carry away the remnants of a thoroughly corrupt era.

Irreverence is all that’s ‘left’

Reader Joseph Librizzi sees a deeper meaning in many American conflicts. He writes, “The heart of the modern Left is a lack of reverence. Nothing higher than ordinary consciousness, nothing sacred.

“The examples abound. Obama’s word games and lack of leadership, Katie Couric and her deceptive editing: it is manipulation of others, disrespect and an arrogant relation to the truth.”

Trump sex poll is full of sheet

Headline: “Only 1% of Americans Say They Would Sleep with Donald Trump, and Just 19% Would Do It for $1,000,000.”

Two thoughts: First, maybe poll respondents rightly saw the question as reprehensible, so ignored it. Second, with such bottom-fishing, CAFE won’t live long enough to become old media.

Making Islam invisible

President Obama and Attorney General Loretta Lynch are not alone in foolishly trying to deny the links to Islam in terrorist atrocities.

The deniers also are heavily represented among New York politicians.

Long Island Congresswoman Kathleen Rice is sending out Islam-free odes to gay and lesbians. “The hate-inspired attack on Orlando’s LGBT community broke our hearts,” she writes. … “To truly honor the victims and survivors of this despicable act we must do more than send thoughts and prayers. Moments of silence are not enough. We need to take action to keep guns out of dangerous hands.”

In fact, the shooter, Omar Mateen, never mentioned “hate” for gays in his calls to cops. Rather, he told the 911 operator, “I pledge of allegiance to Abu Bakr al-Baghdadi of the Islamic State,” then repeated it.

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But Rice would be drummed out of the Democratic Party as a bigot if she dared to connect the dots to radical Islam. Thou shalt not be honest these days.

Like Rice, two Dems in the city council stretched the gay theme to nonsense. Voting for a bill to require all single-occupancy public restrooms to be gender-neutral, Daniel Dromm of Queens and Jumaane Williams of Brooklyn cited the Orlando massacre, saying it was evidence that equal rights for the LGBTQ community still has a long way to go.

So, if Mateen had carried out his massacre in a straight nightclub, apparently there would be no need for the restroom bill. Or would they just make up some other reason so they could deny the link to Islam?